What are Number Talks?

Number Talks are short 5- to 15-minute conversations about mathematical problems, the topic of which is selected by the teacher with the intention of helping students consolidate their understanding of mathematical concepts. This strategy can be implemented at the elementary or secondary level, and it is effective for all students, including those with learning disabilities (LDs).

The problems discussed during number talks must be chosen judiciously in order to allow students with different proficiency levels to actively participate. Once a student has found a solution to the problem, they are encouraged to share it with the class. However, students do not raise their hands; instead, they use an agreed-upon hand signal, such as holding a fist to their chest and raising a thumb, to show that they are ready to share their solution.

Number Talks allow for mathematical exchanges between the teacher and students, and among small groups of students. These exchanges put everyone on an even playing field, as all students are encouraged to participate and make sense of the problem in their own way, and students of all levels of proficiency are given an opportunity to verbalize the steps that they used to solve the problem.

The Teacher’s Role in Number Talks

In a Number Talk, the teacher acts as a facilitator, taking notes (on chart paper, blackboard, or interactive whiteboard) about the various methods and answers provided by students. The teacher also encourages students to verbalize their process by asking prompting questions such as the following.

How did you get your answer?

Why did you use this process?

Who would like to share their steps?

Did anyone solve the problem in a different way?

Which strategies seem the fastest or most efficient?

Benefits of Number Talks

For students with LDs who have difficulty with working memory or remembering number facts, Number Talks are a beneficial strategy that can lead to reduced math anxiety and increased confidence.

Students move away from memorisation and toward mathematical reasoning;

All students have time to reflect;

Students are not distracted or intimidated by raised hands;

Students interact and learn from one another;

Errors are treated as learning opportunities, which creates a safe environment for risk-taking;

Students accept or critique the reasoning of others;

Each student has a chance to share their thought process and solve the problem;

Students verbalize their reasoning to each other;

Students are exposed to multiple strategies to solve the problem;

Feedback is immediate, either from the teacher or other students.

These benefits also apply to students with LDs. For example, many of these students have difficulty with mathematical terminology, and Number Talks allow them to express their ideas in their own words. Similarly, students with LDs may struggle with fine motor control, making it difficult to write their solutions on paper; in Number Talks, where there is a focus on verbalization, these students can participate more easily. Furthermore, students with LDs often struggle with multi-step problems, but verbalization in Number Talks can help them consolidate their understanding of the procedures at the same time as improving their ability to self-monitor while solving the problem.

How to Implement Number Talks in the Classroom?

Elementary

For the elementary level, here is an example of an observation activity:

Ask students to work in small groups to examine the following patterns and then explain what they see. Students should find different ways to count the black dots, and use different equations to express their calculation.

Here is the pattern before students work on it:

Here are the possible answers that students may produce:

Although this is a simple exercise, observation is the first strategy required to solve any problem. It is interesting to see how different students approach the same problem, and their different ways to arrive at the same answer. A problem such as this can stimulate a rich conversation and may serve as a starting point for other, more complex patterns, and for generating algebraic equations.

Secondary

For the secondary level, here is an example of an algebra problem to introduce the quadratic equation (adapted from an activity on Sara Vanderwerf’s blog. Click here to access this blog.).

Here is a pattern of ducks:

Ask students to work in small groups and discuss an equation that could be generated to predict how many ducks would be in the 43rd image. Provide a table such as the one below.

n

Show your work

# of ducks

1

2

3

4

…

43

Equation:

Student will most likely find multiple ways to tackle the problem. Here are two possibilities:

This number talk allows student to have different ways of viewing the problem and different ways of solving it. Students use their critical thinking skills and have their approaches validated by the group. This type of exercise also allows students to apply multiple mathematical concepts within one problem.

Linda Mathieu started her career in Elliot Lake, teaching math and science at the secondary level. From there, she moved to Marathon to teach French at the secondary level before becoming an educational consultant for the Ontario Ministry of Education, leading secondary reform in science and mathematics. She offered teachers in the north-west region of the province tools and accommodations to support students with special education needs in mathematics. Throughout these years, Linda contributed as an author to the Connections in Math series published by Guérin. She returned to the classroom for a few years as a math and science teacher in Thunder Bay. As online and distance courses began to take root, she taught lessons via videoconference and then for the Consortium d’apprentissage virtuel de langue française de l’Ontario (CAVLFO). In this role, Linda adapted certain courses for students with learning disabilities. She completed her career with CAVLFO after seven years, and is now enjoying her retirement.